Pat C, Pat H, Mike, Matthew, David, Sean, Jeffrey, Ferenc, Azamat, and Rich, (01)
I'll start with the Pat-vs-Pat notes, some of which were posted
in different threads, but which are fundamental to this thread: (02)
PC> ... it now seems to me that we can distinguish the meaning
> of "meaning" in math and in computational ontology (the computer
> technology). From this, it appears that the notion of "primitives"
> as I consider them to be useful in ontologies dealing with real-world
> entities may have only an analogical relation (or no relation at all)
> to the elements used in mathematical theories. (03)
I agree that meaning in natural languages is based on much broader
principles and mechanisms than meaning in formal axioms. Even in
mathematics, we have to distinguish the abstract patterns of *pure*
math from the use of those patterns in *applied* math. (04)
As soon as we move from informal semantics to formal ontology,
we are in the realm of applied mathematics. But the terminology
used in applied math is definitely related to the terminology used
in ordinary languages -- usually the *specialized* terminology,
not the common words. (05)
PC> I have often (when trying to be careful) used the term "intended
> meaning" to emphasize that the "meaning" of an ontology term should
> be what the ontologist intended it to be (unless s/he made a logical
> error -- which should be detectable by testing). (06)
I agree. But computer algorithms only deal with formal symbols,
and it's irrelevant whether those symbols came from pure or applied
math. The computer has no access to what's in the head of the
programmer or ontologist. (07)
JFS>>> I was trying to say that terms specified by imagery are
>>> family resemblance terms that cannot be defined by necessary
>>> and sufficient conditions. (08)
PC>>> Agreed - they cannot be defined by necessary and sufficient
>>> conditions, and I have never said and have tried hard to avoid
>>> implying that they are... (09)
PH>> Well then, you have to give us some idea of what you ARE saying.
>> Let me summarize so as to reveal my confusion. You insist that
>> there is, or will be, a clear distinction between primitive
>> concepts in the FO and others. The others will be 'defined in
>> terms of' the primitives. (010)
PC> Correct, as far as the FOL elements of the ontology are concerned.
> But (1) there may also be procedural code that adds to the
> specificity of the interpretation that a computer will place on
> the ontology elements... (011)
But *every* program on a digital computer can be formalized in FOL.
I agree that some things are easier to specify procedurally than
declaratively. I also agree that a hand-coded program can be more
efficient than one that has been derived from a set of axioms. (012)
But every function computed by a program can be specified by the
constraints on its inputs and outputs. There is no magic in
programming: no program can embody any "meaning" that goes
beyond or outside what is or can be specified in axioms. (013)
PC> (2) the linguistic documentation may provide additional information,
> such as reference to well-known instances of types, that help the
> **human ontologist or programmer** to properly interpret and properly
> use the type or relation. (014)
I agree. But any meaning that cannot be specified in axioms cannot
be programmed on a computer or be used in a formal ontology. (015)
PC> (3) the intended meanings of each relation has to be specified
> by rules describing the logical inferences that can be calculated
> for an assertion using that relation. (016)
As soon as you have rules, you have a specification that can be
formalized in axioms and be programmed on a computer. (017)
PC> Perhaps the most important difference between a computational
> ontology and a mathematical theorem is that the ontology is only
> valuable if used in some practical application that references
> entities *outside* of the ontology itself (math theories may also
> be intended to model real-world entities, but don’t have to). (018)
You're talking about the distinction between pure math and applied
math. But for a computer, that distinction is irrelevant. The
algorithms process the symbols of applied math in exactly the same
way that they process the symbols of pure math. (019)
Some other comments: (020)
MB> That [proposal for a repository with a hierarchy of theories]
> sounds eminently doable, and I would certainly want to be involved
> with such a thing. Maybe this could be aligned with the Open
> Ontology Repository work in some way? (021)
I agree. (022)
MB> The stuff I put together for the EDM Council Semantics Repository
> may be a useful picture of part of the problem space - see
> http://www.hypercube.co.uk/edmcouncil under "Global Terms".
> This is a rough and ready starting point for the simple terms I
> wanted to derive industry-specific terms from. (023)
Terminology is an *extremely* important starting point for an ontology.
The terminologists have been doing a very large part of the ground work
for over a century. Their results aren't as precisely specified, but
they are exactly the right terms that we must specify. The total
number of such terms is in the millions. (Some of them are single
polysyllable words, but most of them are short phrases of two or
more words that are critical to the subject matter.) (024)
JFS>> But note that Matthew's approach had almost no similarity to
>> what Pat C has proposed. He and his group developed an ISO 15926
>> over a period of years by an incremental approach of solving one
>> specific problem at a time. (025)
MW> That's not quite right. It was the same problem, integrating
> data from a multitude (up to hundreds) of engineering systems
> to support major process assets like offshore platforms throughout
> their life. (026)
The number of problems is huge. We have *all* been talking about
the "same problem" of "integrating data from a multitude (up to
hundreds) of engineering systems." But note that the words you
used where engineering *terminologies*, not a list of general
words, such as the 2148 from Longman's. (027)
MW> What was incremental was the reworking of the model using
> different foundations until we discovered 4D through Chris
> Partridge's kind offices. We then found we had discovered
> something that met our needs (and I've been going on about
> it ever since). (028)
That's fine. But note that the basis for the 4D ontology is
what Pat H. was talking about, not what Pat C. was saying. (029)
MW> Most of Barry's critique is in fact spurious or wrong. I wrote
> a rebuttal of his critique, which is also available from Wikipedia:
http://www.matthew-west.org.uk/documents/Reponse%20to%20Barry%20Smith%20Comments%20on%20ISO%2015926.htm (030)
OK. As I said, I don't want to get into that debate right now.
But I agree with your point about the very strong similarities
between data models and formal ontology. (031)
MW> Data models have roughly the same expressive power as
> Description Logics, without allowing instances in the ontology,
> so it is quite reasonable to see data models as a type of ontology,
> as Leo Orbst allowed in his analysis of different sorts of ontology. (032)
Actually, the STEP notation you're using has the expressive power
of full first-order logic. The SQL WHERE clause also uses full FOL. (033)
MW> One of my personal rules is not to develop a standard without the
> potential customer for the standard paying. Developing standards
> as a hobby is a good way to get bad standards. Now if you want to
> call it research then that is fine. (034)
I very strongly agree with that point. That is why Cyc never
started to make money until they stopped doing "pure" research
{as a result of the gov't pulling the plug on their funding). (035)
DE> I'm working the interoperability issue from bottom to top.
>
> Ontology (top)
> Taxonomy
> Naming standards (bottom) (036)
That's good. Note that you're starting with the terminologies
used in your applications. That is what Mike B. advocated,
and I strongly agree. (037)
DE> I've directly experienced the value that "good names" brings
> to a software project...
>
> Example: if you look at code & see two dates are being added
> together, you instantly know that's a defective line of code. (038)
I agree. And note that you can specify that information in a
type hierarchy for the terminology and in the "signature" and
cardinality of the various relations (i.e., what is usually
represented in an Entity-Relationship diagram). I have often
said that the Semantic Webbers made a major blunder in *not*
building on the techniques developed by the software engineers. (039)
SB> It is not uncommon when characterising mathematical systems
> to start with one set of axioms and demonstrate that another set
> of axioms is equivalent. (040)
I strongly approve of using mathematical techniques. But note
that starting with axioms makes the problem undecidable. If you
start with one or more models of those axioms, the problem becomes
much easier to deal with. (041)
SB> Might I suggest following up on the group of mathematicians
> that published under the name of Nicolas Bourbaki. (042)
I have a high regard for the brilliant mathematicians who published
under that name, but they had some extremely misguided principles
that made their books unusable for teaching: they believed that
all diagrams should be abolished. (043)
JAS> But now consider (from an different J. Sowa source) :
>
> - An Elephant is a species
> - Clyde is an elephant
> - Therefore Clyde is a species (044)
I cited that as a bad example. But the first sentence did
not have the article 'an'. If you say 'Elephant is a species',
that indicates that you mean the term 'elephant' as the name
of a species rather than a reference to an individual. If you
are careful to make that distinction, you can use the same verb. (045)
In any case, it's important to use formal notations that make
those distinctions clear. One problem with using a simplified
notation (as many people do in their so-called ontologies)
is that they get hopelessly confused. (046)
FK> Re: naming standards. Would the principle of Hungarian
> notation adopted suitably be of any help?
> http://en.wikipedia.org/wiki/Hungarian_notation (047)
That convention, which includes type information in the name,
has been used in mathematics for centuries by using different
alphabets, fonts, or capitalization. It's useful with a small,
fixed number of types, but it gets unwieldy with a large number. (048)
AA> While the Forum is hotly discussing if the Foundation Ontology
> and Semantic Interoperability are valid concepts, the EU set up
> the Semantic Interoperability Center Europe 3 years ago,
> http://www.semic.eu/semic/ (049)
That's useful. But note that the main thing they're emphasizing
is the importance of a standard *terminology* and classification.
Descartes, Pascal, Leibniz, Linnaeus, and L'Académie française
noticed point that four centuries ago. Some of it (notably by
L'Académie française) was misguided, but the specialized
terminologies of various fields are essential for ontology. (050)
RC> The organization of WordNet, and its success in mapping out
> synsets from English common usage, shows that we communicate
> very inexactly, or in an "underspecified" way, as some writers
> like to say. (051)
That point was noted by Kant, who observed that "natural concepts"
can never be fully specified by necessary and sufficient conditions
and that only words defined by convention (as in mathematics) can
be precisely specified. Wittgenstein emphasized it very strongly,
but nobody who ever studied the details ever refuted that point. (052)
RC> John Sowa seems to believe that the other 10-20% of English
> words were created opportunistically in language games... (053)
I'm happy that you like some of the things I said, but please
don't attribute any statement to me without an exact quotation.
In any case, I approve of the conclusion: (054)
RC> ... there has to be some limit on complexity of vocabularies,
> conceptual universes, and relational associations. (055)
A more accurate summary of what I said in this and other notes
can also be used to summarizes the basic points I've been making: (056)
1. It's very difficult for children and even harder for adults
to learn a huge vocabulary of words. (057)
2. It's much easier for people to learn a few thousand words
and modify their meaning by context and usage or by adding
a qualifying word or phrase to specify finer distinctions. (058)
3. A subset of common words (such as Longman's list) is so
vague and "squishy" that the dictionary editors can use
it to give a "rough" idea of what other words mean. (059)
4. But those squishy primitives and the rough definitions
based on them are hopeless as a foundation for a formal
ontology or for a precise specification of computer systems. (060)
5. A much better starting point for formal ontologies are
the terminologies that have been standardized by experts
in various branches of science, engineering, medicine.... (061)
6. But for precise reasoning, the terms in point #5 must be
supplemented with detailed axioms stated in some version of
logic. Those logics could use a wide range of notations,
including diagrams such as UML or many kinds of controlled
natural languages. (062)
Note Point #2 above. The idea of adding a prefix to the name
is just a spelling convention for specifying the modifier.
It's not surprising that Hungarians like it, because Hungarian
is an "agglutinative" language that does things like that. (063)
John Sowa (064)
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